Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
An example where the codomain is explicitly specified.
sage: n = m.apply_map(lambda x:x%3, GF(3))
sage: n.parent()
Full MatrixSpace of 10000 by 10000 sparse matrices over Finite Field of size 3
sage: n[1,2]
2
If we didn’t specify the codomain, the resulting matrix in the above case ends up over ZZ again:
sage: n = m.apply_map(lambda x:x%3)
sage: n.parent()
Full MatrixSpace of 10000 by 10000 sparse matrices over Integer Ring
sage: n[1,2]
2
If self is subdivided, the result will be as well:
sage: m = matrix(2, 2, [0, 0, 3, 0])
sage: m.subdivide(None, 1); m
[0|0]
[3|0]
sage: m.apply_map(lambda x: x*x)
[0|0]
[9|0]
If the map sends zero to a non-zero value, then it may be useful to get the result as a dense matrix.
sage: m = matrix(ZZ, 3, 3, [0] * 7 + [1,2], sparse=True); m
[0 0 0]
[0 0 0]
[0 1 2]
sage: parent(m)
Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring
sage: n = m.apply_map(lambda x: x+polygen(QQ), sparse=False); n
[ x x x]
[ x x x]
[ x x + 1 x + 2]
sage: parent(n)
Full MatrixSpace of 3 by 3 dense matrices over Univariate Polynomial Ring in x over Rational
TESTS:
sage: m = matrix([], sparse=True)
sage: m.apply_map(lambda x: x*x) == m
True
sage: m.apply_map(lambda x: x*x, sparse=False).parent()
Full MatrixSpace of 0 by 0 dense matrices over Integer Ring
Check that we don’t unnecessarily apply phi to 0 in the sparse case:
sage: m = matrix(QQ, 2, 2, range(1, 5), sparse=True)
sage: m.apply_map(lambda x: 1/x)
[ 1 1/2]
[1/3 1/4]
Test subdivisions when phi maps 0 to non-zero:
sage: m = matrix(2, 2, [0, 0, 3, 0])
sage: m.subdivide(None, 1); m
282 Chapter 11. Base class for sparse matrices